A researcher selects a sample of 1000 people to investigate the relationship bet

Question

A researcher selects a sample of 1000 people to investigate the relationship between ethnicity (Caucasian, African-American, Hispanic/Latino and Other) and registering to vote (registered to vote, not registered to vote). If the researcher obtains a Chi2 = 8.37, what is the appropriate statistical decision for the test? Assume p < .05.

A. Reject the null hypothesis and conclude that there is no significant relationship between ethnicity and registering to vote. B. Reject the null hypothesis and conclude that there is a significant relationship between ethnicity and registering to vote. C. Fail to reject the null hypothesis and conclude that there is a significant relationship between ethnicity and registering to vote. D. Fail to reject the null hypothesis and conclude that there is no significant relationship between ethnicity and registering to vote.

Explanation / Answer

Let a1 and a2 be the set of possible values ethnicity and vote registration could have.

Hence, a1 = { Caucasian, African-American, Hispanic/Latino, Other}

and a2 = {Yes, No}

Degrees of freedom(df) = (n1-1) * (n2-1) where n1 and n2 are the size of sets a1 and a2 respectively.

Hence df in our case = (4-1) * (2-1) = 3

Given df=3 and p<0.05, we get the tabulated chi-square value as: 7.8147 [From standard chi-square table with degrees of freedom as the column index and p value as the row index]

Conclusion: Since the calculated chi-square value(8.37) is higher than the tabulated chi-square value, by property of CHi-square test, reject the null hypothesis. As per convention, the null hypothesis is established assuming that there is no relation between the two sets. Hence in our case, the null hypothesis is that there is no relationship between etnicity and registering to vote, which we are rejecting.

Hence Option B is the right answer.

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